Asymptotic variance–covariance matrices for the linear structural model

Abstract

In recent years there has been renewed interest in errors in variables regression models, where there are errors in the predictor variables as well as the dependent variable. Despite recent advances, the theory of the simple linear errors in variables model does not yet match the well known methodology of simple linear regression. This paper fills one of these gaps by presenting results for the straight line errors in variables model that will enable a practitioner to estimate not only the parameters of the model but also the approximate variances of these estimates. Attention is therefore focused on the variances of the model and the extraction of estimates. The presentation adopts a method of moments approach, but connections are made with the method of least squares and the maximum likelihood approach.